Advertisement

Polygonal Meshes

  • Jakob Andreas BærentzenEmail author
  • Jens Gravesen
  • François Anton
  • Henrik Aanæs

Abstract

The polygonal mesh representation is one of the most general and most used representations of geometric data. A large part of the success of meshes is the simplicity of the representation combined with the fact that computers are increasingly able to deal with the large amounts of data needed in order to represent a smooth surface using polygons.

In this chapter, we cover the basic notions of a polygonal meshes: faces, edges, vertices. We move on to data sources for polygonal meshes and common issues when meshes are considered to be sampled representations of smooth surfaces. Also, we discuss the common basic operations for manipulation of meshes, e.g., edge collapse, edge flipping, splitting of edges and faces, etc.

Finally, we discuss concrete data structures for polygonal meshes. In particular, the indexed face set representation, the halfedge representation, and the quad edge representation are covered. These are some of the most useful and generic representations for polygonal meshes.

Keywords

Voronoi Diagram Delaunay Triangulation Implicit Surface Triangle Mesh Polygonal Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Grossman, J.P., Dally, W.J.: Point sample rendering. In: Proceedings of the 9th Eurographics Workshop on Rendering, June pp. 181–192 (1998) Google Scholar
  2. 2.
    Pfister, H., Zwicker, M., van Baar, J., Gross, M.: Surfels: surface elements as rendering primitives. In: Proceedings of SIGGRAPH 2000, pp. 335–342 (2000) Google Scholar
  3. 3.
    Zwicker, M., Pfister, H., van Baar, J., Gross, M.: EWA splatting. IEEE Trans. Vis. Comput. Graph. 8(3), 223–238 (2002) CrossRefGoogle Scholar
  4. 4.
    Dachsbacher, C., Vogelgsang, C., Stamminger, M.: Sequential point trees. ACM Trans. Graph. 22(3), 657–662 (2003). doi: 10.1145/882262.882321 CrossRefGoogle Scholar
  5. 5.
    Botsch, M., Hornung, A., Zwicker, M., Kobbelt, L.: High-quality surface splatting on today’s GPUs. In: Proceedings of Symposium on Point-Based Graphics, pp. 17–24 (2005) Google Scholar
  6. 6.
    Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M.: Shape modeling with point-sampled geometry. ACM Trans. Graph. 22(3), 641–650 (2003) CrossRefGoogle Scholar
  7. 7.
    Pauly, M., Gross, M.: Spectral processing of point-sampled geometry. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 379–386 (2001) Google Scholar
  8. 8.
    Hoffmann, C.M.: Geometric and Solid Modeling. Morgan Kaufmann, San Mateo (1989) Google Scholar
  9. 9.
    Chazelle, B.: Triangulating a simple polygon in linear time. Discrete Comput. Geom. 6, 485–524 (1991) MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, pp. 209–216 (1997) Google Scholar
  11. 11.
    Zorin, D., Schröder, P., DeRose, T., Kobbelt, L., Levin, A., Sweldens, W.: Subdivision for modeling and animation. Technical Report, SIGGRAPH 2000 Course Notes (2000) Google Scholar
  12. 12.
    Baumgart, B.G.: Winged edge polyhedron representation. Technical Report, Stanford University (1972) Google Scholar
  13. 13.
    Mantyla, M.: Introduction to Solid Modeling. Freeman, New York (1988) Google Scholar
  14. 14.
    Botsch, M., Steinberg, S., Bischoff, S., Kobbelt, L.: OpenMesh-a generic and efficient polygon mesh data structure. In: OpenSG Symposium (2002) Google Scholar
  15. 15.
  16. 16.
    Guibas, L., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4, 74–123 (1985) zbMATHCrossRefGoogle Scholar
  17. 17.
    Lienhardt, P.: Extension of the notion of map and subdivisions of a three-dimensional space. In: STACS 88 (Bordeaux, 1988). Lecture Notes in Comput. Sci., vol. 294, pp. 301–311. Springer, Berlin (1988) CrossRefGoogle Scholar
  18. 18.
    Joy, K.I., Legakis, J., MacCracken, R.: Data structures for multiresolution representation of unstructured meshes. In: Farin, G., Hagen, H., Hamann, B. (eds.) Hierarchical Approximation and Geometric Methods for Scientific Visualization. Springer, Heidelberg (2002) Google Scholar
  19. 19.
    Campagna, S., Kobbelt, L., Seidel, H.P.: Directed edges—a scalable representation for triangle meshes. J. Graph. Tools 3(4), 1–12 (1998) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Jakob Andreas Bærentzen
    • 1
    Email author
  • Jens Gravesen
    • 2
  • François Anton
    • 1
  • Henrik Aanæs
    • 1
  1. 1.Department of Informatics and Mathematical ModellingTechnical University of DenmarkKongens LyngbyDenmark
  2. 2.Department of MathematicsTechnical University of DenmarkKongens LyngbyDenmark

Personalised recommendations